/* ----------------------------------------------------------------------  
* Copyright (C) 2010 ARM Limited. All rights reserved.  
*  
* $Date:        29. November 2010  
* $Revision: 	V1.0.3  
*  
* Project: 	    CMSIS DSP Library  
* Title:	    arm_dct4_q31.c  
*  
* Description:	Processing function of DCT4 & IDCT4 Q31.  
*  
* Target Processor: Cortex-M4/Cortex-M3
*  
* Version 1.0.3 2010/11/29 
*    Re-organized the CMSIS folders and updated documentation.  
*   
* Version 1.0.2 2010/11/11  
*    Documentation updated.   
*  
* Version 1.0.1 2010/10/05   
*    Production release and review comments incorporated.  
*  
* Version 1.0.0 2010/09/20   
*    Production release and review comments incorporated.  
* -------------------------------------------------------------------- */ 
 
#include "arm_math.h" 
 
/**  
 * @addtogroup DCT4_IDCT4  
 * @{  
 */ 
 
/**  
 * @brief Processing function for the Q31 DCT4/IDCT4. 
 * @param[in]       *S             points to an instance of the Q31 DCT4 structure. 
 * @param[in]       *pState        points to state buffer. 
 * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer. 
 * @return none. 
 * \par Input an output formats:  
 * Input samples need to be downscaled by 1 bit to avoid saturations in the Q31 DCT process,  
 * as the conversion from DCT2 to DCT4 involves one subtraction.  
 * Internally inputs are downscaled in the RFFT process function to avoid overflows.  
 * Number of bits downscaled, depends on the size of the transform.  
 * The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:   
 *  
 * \image html dct4FormatsQ31Table.gif  
 */ 
 
void arm_dct4_q31( 
  const arm_dct4_instance_q31 * S, 
  q31_t * pState, 
  q31_t * pInlineBuffer) 
{ 
  uint16_t i;                                    /* Loop counter */ 
  q31_t *weights = S->pTwiddle;                  /* Pointer to the Weights table */ 
  q31_t *cosFact = S->pCosFactor;                /* Pointer to the cos factors table */ 
  q31_t *pS1, *pS2, *pbuff;                      /* Temporary pointers for input buffer and pState buffer */ 
  q31_t in;                                      /* Temporary variable */ 
 
 
  /* DCT4 computation involves DCT2 (which is calculated using RFFT)  
   * along with some pre-processing and post-processing.  
   * Computational procedure is explained as follows:  
   * (a) Pre-processing involves multiplying input with cos factor,  
   *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))  
   *              where,  
   *                 r(n) -- output of preprocessing  
   *                 u(n) -- input to preprocessing(actual Source buffer)  
   * (b) Calculation of DCT2 using FFT is divided into three steps:  
   *                  Step1: Re-ordering of even and odd elements of input.  
   *                  Step2: Calculating FFT of the re-ordered input.  
   *                  Step3: Taking the real part of the product of FFT output and weights.  
   * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:  
   *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)  
   *                        where,  
   *                           Y4 -- DCT4 output,   Y2 -- DCT2 output  
   * (d) Multiplying the output with the normalizing factor sqrt(2/N).  
   */ 
 
        /*-------- Pre-processing ------------*/ 
  /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */ 
  arm_mult_q31(pInlineBuffer, cosFact, pInlineBuffer, S->N); 
  arm_shift_q31(pInlineBuffer, 1, pInlineBuffer, S->N); 
 
  /* ----------------------------------------------------------------  
   * Step1: Re-ordering of even and odd elements as  
   *             pState[i] =  pInlineBuffer[2*i] and  
   *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2  
   ---------------------------------------------------------------------*/ 
 
  /* pS1 initialized to pState */ 
  pS1 = pState; 
 
  /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */ 
  pS2 = pState + (S->N - 1u); 
 
  /* pbuff initialized to input buffer */ 
  pbuff = pInlineBuffer; 
 
  /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */ 
  i = S->Nby2 >> 2u; 
 
  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
   ** a second loop below computes the remaining 1 to 3 samples. */ 
  do 
  { 
    /* Re-ordering of even and odd elements */ 
    /* pState[i] =  pInlineBuffer[2*i] */ 
    *pS1++ = *pbuff++; 
    /* pState[N-i-1] = pInlineBuffer[2*i+1] */ 
    *pS2-- = *pbuff++; 
 
    *pS1++ = *pbuff++; 
    *pS2-- = *pbuff++; 
 
    *pS1++ = *pbuff++; 
    *pS2-- = *pbuff++; 
 
    *pS1++ = *pbuff++; 
    *pS2-- = *pbuff++; 
 
    /* Decrement the loop counter */ 
    i--; 
  } while(i > 0u); 
 
  /* pbuff initialized to input buffer */ 
  pbuff = pInlineBuffer; 
 
  /* pS1 initialized to pState */ 
  pS1 = pState; 
 
  /* Initializing the loop counter to N/4 instead of N for loop unrolling */ 
  i = S->N >> 2u; 
 
  /* Processing with loop unrolling 4 times as N is always multiple of 4.  
   * Compute 4 outputs at a time */ 
  do 
  { 
    /* Writing the re-ordered output back to inplace input buffer */ 
    *pbuff++ = *pS1++; 
    *pbuff++ = *pS1++; 
    *pbuff++ = *pS1++; 
    *pbuff++ = *pS1++; 
 
    /* Decrement the loop counter */ 
    i--; 
  } while(i > 0u); 
 
 
  /* ---------------------------------------------------------  
   *     Step2: Calculate RFFT for N-point input  
   * ---------------------------------------------------------- */ 
  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ 
  arm_rfft_q31(S->pRfft, pInlineBuffer, pState); 
 
  /*----------------------------------------------------------------------  
   *  Step3: Multiply the FFT output with the weights.  
   *----------------------------------------------------------------------*/ 
  arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N); 
 
  /* The output of complex multiplication is in 3.29 format.  
   * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */ 
  arm_shift_q31(pState, 2, pState, S->N * 2); 
 
  /* ----------- Post-processing ---------- */ 
  /* DCT-IV can be obtained from DCT-II by the equation,  
   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)  
   *       Hence, Y4(0) = Y2(0)/2  */ 
  /* Getting only real part from the output and Converting to DCT-IV */ 
 
  /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */ 
  i = (S->N - 1u) >> 2u; 
 
  /* pbuff initialized to input buffer. */ 
  pbuff = pInlineBuffer; 
 
  /* pS1 initialized to pState */ 
  pS1 = pState; 
 
  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ 
  in = *pS1++ >> 1u; 
  /* input buffer acts as inplace, so output values are stored in the input itself. */ 
  *pbuff++ = in; 
 
  /* pState pointer is incremented twice as the real values are located alternatively in the array */ 
  pS1++; 
 
  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
   ** a second loop below computes the remaining 1 to 3 samples. */ 
  do 
  { 
    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 
    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 
    in = *pS1++ - in; 
    *pbuff++ = in; 
    /* points to the next real value */ 
    pS1++; 
 
    in = *pS1++ - in; 
    *pbuff++ = in; 
    pS1++; 
 
    in = *pS1++ - in; 
    *pbuff++ = in; 
    pS1++; 
 
    in = *pS1++ - in; 
    *pbuff++ = in; 
    pS1++; 
 
    /* Decrement the loop counter */ 
    i--; 
  } while(i > 0u); 
 
  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.  
   ** No loop unrolling is used. */ 
  i = (S->N - 1u) % 0x4u; 
 
  while(i > 0u) 
  { 
    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 
    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 
    in = *pS1++ - in; 
    *pbuff++ = in; 
    /* points to the next real value */ 
    pS1++; 
 
    /* Decrement the loop counter */ 
    i--; 
  } 
 
 
        /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ 
 
  /* Initializing the loop counter to N/4 instead of N for loop unrolling */ 
  i = S->N >> 2u; 
 
  /* pbuff initialized to the pInlineBuffer(now contains the output values) */ 
  pbuff = pInlineBuffer; 
 
  /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */ 
  do 
  { 
    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ 
    in = *pbuff; 
    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); 
 
    in = *pbuff; 
    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); 
 
    in = *pbuff; 
    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); 
 
    in = *pbuff; 
    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31)); 
 
    /* Decrement the loop counter */ 
    i--; 
  } while(i > 0u); 
 
} 
 
/**  
   * @} end of DCT4_IDCT4 group  
   */ 
